Answer:
The value of the lesser integer is [tex]28[/tex]
Step-by-step explanation:
Let two consecutive positive integers be [tex]x,x+1[/tex].
Product of two consecutive positive integers = [tex]x(x+1)=x^2+x[/tex]
Also, product of two consecutive positive integers is 812
So,
[tex]x^2+x=812\\x^2+x-812=0\\x^2+29x-28x-812=0\\x(x+29)-28(x+29)=0\\(x-28)(x+29)=0\\x=28,-29[/tex]
As [tex]x[/tex] is a positive integer,
[tex]x=-29[/tex] is rejected.
So,
[tex]x=28\\x+1=28+1=29[/tex]
Two positive integers are [tex]28,29[/tex]
The value of the lesser integer is [tex]28[/tex]
